Finite Group Databasebeta

← #50304031

Subgroups — #50304031

Order 38220.

168 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊#16838469C211yesmaximal, characteristic, complemented
2C7×C5⋊#10587721C211yesmaximal, characteristic, complemented
3C5×#16838480C211yesmaximal, characteristic, complemented
4D35×D91C311yesmaximal, characteristic, complemented, Hall
5C5×C7×#63271C2211yescharacteristic, complemented, Hall
6#10587721⋊D7—51nomaximal, Hall
7C5⋊(C7⋊D91)C2×C311yescharacteristic, complemented
8C7×C13×D35C2×C311yescharacteristic, complemented
9C5×C7×D91C2×C311yescharacteristic, complemented
10D5×(C13⋊C3)⋊D7—71nomaximal
11#10587717⋊D5—71nomaximal
12#16838480D511yescharacteristic, complemented
13#16838469—51no—
14C7×#10587721—51no—
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16D7×C5⋊AGL(1,𝔽7)—131nomaximal, Hall
17C5⋊#10587723—71no—
18C5⋊((C13⋊C3)⋊D7)—71no—
19C5⋊#10587721D711yescharacteristic, complemented
20C7×D5×C13⋊C3—71no—
21C5×(C13⋊C3)⋊D7—71no—
22C5×#10587717—71no—
23D7×D91—51noHall
24C7×#63271C2×D511yescharacteristic, complemented, Hall
25D5×D91—71no—
26D13×D35—71no—
27C5⋊(ΓL(1,𝔽8)⋊D7)—131no—
28C7×C5⋊AGL(1,𝔽7)—131no—
29C5×D7×ΓL(1,𝔽8)—131no—
30C5×#63271C2×D711yescharacteristic, complemented
31C5×C7×C13⋊C3—71no—
32C7⋊D91—51no—
33C7×D91C3×D511yescharacteristic, complemented
34C7×C13×D7—51no—
35C2×(C13⋊C3)⋊D7—351no—
36#10587717⋊C2—351no—
37D7×D35—131noHall
38D455—71no—
39D455—71no—
40D455—421no—
41C13×D35C3×D711yescharacteristic, complemented
42C7×D5×C13—71no—
43C5×D91AGL(1,𝔽7)11yescharacteristic, complemented
44C5×C7×D13—71no—
45D5×D13⋊C3—491noHall
46C5×C7×ΓL(1,𝔽8)—131noHall
47C72×C13C2×C3×D511yescharacteristic, complemented, Hall
48D7×AGL(1,𝔽7)—651noHall
49C2×C7×C13⋊C3—351no—
50#10587723—351no—
51#10587721—51no—
52#10587717—71no—
53(C13⋊C3)⋊D7—71no—
54(C13⋊C3)⋊D7—351no—
55C5⋊(C7⋊D7)—131no—
56C7×D35D13⋊C311yescharacteristic, complemented
57C5×C7×D7—131no—
58C5×C7×C13—61no—
59C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic, complemented
60C5×C7×C13C2×C3×D711yescharacteristic, complemented
61C3×D5×D7—911no—
62C2×C5⋊AGL(1,𝔽7)—911no—
63C5⋊(D13⋊C3)—491no—
64D5×C13⋊C3—71no—
65C5×D13⋊C3—491no—
66C2×D91—351no—
67D7×D13—351no—
68ΓL(1,𝔽8)⋊D7—651no—
69D7×ΓL(1,𝔽8)—131no—
70C7×AGL(1,𝔽7)—651no—
71#63271D5×D711yescharacteristic, complemented
72C7×C13⋊C3—71no—
73D5×D13—491noHall
74C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
75C3×D35—911no—
76C3×C7×D5—911no—
77C3×C5×D7—911no—
78C2×C5×ΓL(1,𝔽8)—911no—
79C5⋊AGL(1,𝔽7)—131no—
80C5⋊AGL(1,𝔽7)—911no—
81D72—651noHall
82C5×C13⋊C3—71noHall
83C2×C7×C13—351no—
84D91—351no—
85D91—351no—
86D91—2101no—
87D91C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
88C7×D13—71no—
89C13×D7—51no—
90C2×D13⋊C3—2451noHall
91C7×ΓL(1,𝔽8)—131noHall
92C2×D35—911no—
93D5×D7—911no—
94D65—491no—
95C5×D13—71no—
96D5×C13—71no—
97C3×C5×C7—911no—
98C5×ΓL(1,𝔽8)—131no—
99C7⋊D7—651no—
100C7×D7—51no—
101C7×D7—131no—
102C7×C13—61no—
103C7×C13C2×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
104C7×C13C3×D5×D711yescharacteristic, complemented
105C2×C3×D7—4551no—
106C2×AGL(1,𝔽7)—4551no—
107C2×C13⋊C3—351no—
108D13⋊C3—491no—
109D13⋊C3—2451no—
110C2×C5×C7—911no—
111D35—5461no—
112D35—911no—
113D35—911no—
114D35(C13⋊C3)⋊D711yescharacteristic, complemented
115C5×D7—131no—
116C7×D5—71no—
117C5×C13D7×AGL(1,𝔽7)11yescharacteristic, complemented, Hall
118C2×C3×D5—6371noHall
119C2×D13—2451noHall
120C72D5×D13⋊C311yescharacteristic, complemented, Sylow
121C2×C3×C7—4551no—
122C3×D7—911no—
123C3×D7—4551no—
124C2×ΓL(1,𝔽8)—911no—
125AGL(1,𝔽7)—651no—
126AGL(1,𝔽7)—4551no—
127C13⋊C3—71noHall
128C5×C7—61no—
129C5×C7#10587717⋊C211yescharacteristic, complemented
130C5×C7C2×(C13⋊C3)⋊D711yescharacteristic, complemented
131C2×C3×C5—6371no—
132C3×D5—911no—
133C3×D5—6371no—
134C2×D7—4551no—
135C2×D7—4551no—
136C2×C13—351no—
137D13—71no—
138D13—2451no—
139C3×C7—911no—
140ΓL(1,𝔽8)—131no—
141C2×D5—6371noHall
142C3×C5—911noHall
143C2×C7—351no—
144C2×C7—911no—
145D7—51no—
146D7—131no—
147D7—27301no—
148D7—4551no—
149D7—4551no—
150C13D7×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented, Sylow
151C22×C3—31851noHall
152C2×C5—911no—
153D5—71no—
154D5—6371no—
155C7—61no—
156C7#10587717⋊D511yescharacteristic, complemented
157C7D5×(C13⋊C3)⋊D711yescharacteristic, complemented
158C2×C3—31851no—
159C2×C3—6371no—
160C2×C3—4551no—
161C5#10587721⋊D711yescharacteristic, complemented, Sylow
162C22—31851noSylow
163C3—911noSylow
164C2—351no—
165C2—911no—
166C2—31851no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5⋊#16838469C2semidirect
2. C7×C5⋊#10587721C2semidirect
3. C5×#16838480C2semidirect
4. D35×D91C3semidirect
5. C5×C7×#63271C22semidirect
7. C5⋊(C7⋊D91)C2×C3semidirect
8. C7×C13×D35C2×C3semidirect
9. C5×C7×D91C2×C3semidirect
12. #16838480D5semidirect
15. C5×C72×C13C22×C3semidirect
19. C5⋊#10587721D7semidirect
24. C7×#63271C2×D5semidirect
30. C5×#63271C2×D7semidirect
33. C7×D91C3×D5semidirect
41. C13×D35C3×D7semidirect
43. C5×D91AGL(1,𝔽7)semidirect
47. C72×C13C2×C3×D5semidirect
56. C7×D35D13⋊C3semidirect
59. C5×C7×C13C2×AGL(1,𝔽7)semidirect
60. C5×C7×C13C2×C3×D7semidirect
71. #63271D5×D7semidirect
74. C5×C72C2×D13⋊C3semidirect
87. D91C5⋊AGL(1,𝔽7)semidirect
103. C7×C13C2×C5⋊AGL(1,𝔽7)semidirect
104. C7×C13C3×D5×D7semidirect
114. D35(C13⋊C3)⋊D7semidirect
117. C5×C13D7×AGL(1,𝔽7)semidirect
120. C72D5×D13⋊C3semidirect
129. C5×C7#10587717⋊C2semidirect
130. C5×C7C2×(C13⋊C3)⋊D7semidirect
150. C13D7×C5⋊AGL(1,𝔽7)semidirect
156. C7#10587717⋊D5semidirect
157. C7D5×(C13⋊C3)⋊D7semidirect
161. C5#10587721⋊D7semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5⋊#168384692
C7×C5⋊#105877212
C5×#168384802
D35×D913
#10587721⋊D75
D5×(C13⋊C3)⋊D77
#10587717⋊D57
D7×C5⋊AGL(1,𝔽7)13